OK. Looking at the spiritual rather than the temporal:
Let's just say that OJ was Catholic and repented/had Last Rites before death. What would Catholic teaching be here? Would that be enough, or would he have to go public with his repentance to be properly absolved?
This is just my speculation here (based upon nothing more than what I perceive to be common sense), but I have always thought that repentance and confession of any sin that has involved another person in loss (whether material, psychological, or spiritual), has to entail making those losses good, and repairing whatever damage was done, insofar as the penitent is able. I would think --- and, again, I'd welcome good education on this --- that the priest can and should make such satisfaction, and the penitent's willingness to make that satisfaction, a condition of absolution. Stay with me on this.
I have gotten some "pushback" in discussion with other Catholics on this matter, to the effect that requiring such reparation would involve disclosing the contents of a confession. I really don't think so. To my mind, it says nothing about whether one has been to confession or not. Let's say that I kill someone and bury the body somewhere. There is no evidence of my crime, and the person just goes missing, much to the anguish of their loved ones. Then I get the grace of repentance and confess the murder. Why can the priest not make turning myself in, and suffering the consequences (prison, perhaps even the death penalty, as well as being willing to make the victim's family whole if they pursue a wrongful death civil lawsuit, as the Goldmans did), a condition of administering absolution? If I am absolved, and then make no one aware that I killed the person, I am leaving their family in agony, never knowing what happened to their loved one. They search in vain, and all the while, I'm sitting back knowing what happened, and keeping my mouth shut.
Then take it a step further.
Someone else is charged with the murder, and through circuмstantial evidence, that a jury accepts, that person is convicted of the murder, goes to prison, perhaps even gets the death penalty, and
their estate is sued for wrongful death reparations. All the while, I am just sitting back, letting it happen, and now I've wronged not one person (by murdering them and burying the body), but two, in letting an innocent man take the rap for the murder.
The same holds true if, for instance, I steal someone's car and hide it in my garage. (Maybe I've just always wanted a car like that, and am content to sit in it, in the garage, and have the contentment of finally having such a car.) I then become accused in conscience, go to confession, and confess the sin of stealing the car. Don't I have to give that car back? And if I do, am I supposed to drive it to the person's house in the dead of night and leave the keys on the dashboard, slinking away in the dark and somehow making my way home, all in the name of not revealing that I was the thief, all in the name of not disclosing that I confessed stealing the car? Or do I simply "man up", drive the car to the person's home, knock on the door, say "hey, I stole your car, and I'm sorry I did it, here are the keys, could you please not call the police and tell them I stole it, keep me out of trouble?". That doesn't tell the person that I've been to confession. It simply tells him that I stole his car and I'm bringing it back. I'm entirely at his mercy as to whether he calls the police or not, but that's what I get for having stolen the car. Temporal punishment, as it were.
TLDR, can a priest make restitution, and any consequences that come of it, a condition for absolving a sin that involved another person incurring loss? And if not, why not?